Question

Let `f(x)=2x+3` and `g(x)=x^2-4` and `h(x)=x-3/2`, how do you find g(f(3))?

Answer 1

The answer is : `g(f(3)) = 77`

Firstly, let's find `g(f(x))` :

You have `f(x) = 2x+3` and `g(x) = x^(2) - 4`, so

`g(f(x)) = f^(2)(x) -4 = (2x+3)^(2) -4`

`g(f(x)) = 4x^(2)+12x+9-4=4x^(2)+12x+5`

Now you can calculate `g(f(3))` :

`g(f(3)) = 4*3^(2) + 12*3 + 5 = 36 + 36 + 5 = 77`

Answer 2

Have a look. I think it is ok, although I didn't used `h(x)`...